%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL186-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:07:02 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.72s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 47 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(implies(not(p),implies(p,q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
~ theorem(implies(not(p),implies(p,q))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0,X1] : axiom(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ axiom(implies(X1,X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f34,plain,
! [X0,X1] :
( ~ axiom(X1)
| ~ axiom(implies(X1,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f25,f16]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ theorem(X1)
| theorem(X2)
| ~ axiom(X0)
| ~ axiom(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f34,f18]) ).
fof(f39,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f41,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f39]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ axiom(X1)
| theorem(X2)
| ~ axiom(X0)
| ~ axiom(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f36,f16]) ).
fof(f58,plain,
! [X0,X1] :
( ~ axiom(X1)
| ~ axiom(X0)
| ~ axiom(implies(X0,implies(X1,implies(not(p),implies(p,q))))) ),
inference(resolution,[status(thm)],[f53,f19]) ).
fof(f107,plain,
! [X0] :
( ~ axiom(implies(not(p),X0))
| ~ axiom(implies(X0,implies(p,q))) ),
inference(resolution,[status(thm)],[f58,f41]) ).
fof(f112,plain,
! [X0] : ~ axiom(implies(or(X0,not(p)),implies(p,q))),
inference(resolution,[status(thm)],[f107,f11]) ).
fof(f117,plain,
$false,
inference(resolution,[status(thm)],[f112,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL186-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n009.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Mon Sep 21 00:09:57 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.21/0.66 % Drodi V4.1.1
% 0.21/0.72 % Refutation found
% 0.21/0.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.74 % Elapsed time: 0.088265 seconds
% 0.21/0.74 % CPU time: 0.375079 seconds
% 0.21/0.74 % Total memory used: 70.166 MB
% 0.21/0.74 % Net memory used: 69.418 MB
%------------------------------------------------------------------------------